Question

ARVIND bought two articles for rupees 1200 each. He sold one of them at a profit of x% and other at a profit of x² % .IF total profit is rupees 360,find the selling price of each of the articles.

Answer 1

$$\begin{gathered} \mathrm{CP}\mathrm{of}\mathrm{first}\mathrm{article}=\mathrm{Rs}1200 \\ \mathrm{Profit}\%=x\% \\ \Rightarrow \left[\frac{\mathrm{profit}}{\mathrm{CP}}\times 100\right]\%=x\% \\ \Rightarrow \left[\frac{\mathrm{profit}}{1200}\times 100\right]=x \\ \Rightarrow \mathrm{profit}=\mathrm{Rs}12x \\ \mathrm{CP}\mathrm{of}\mathrm{second}\mathrm{article}=\mathrm{Rs}1200 \\ \mathrm{Profit}\%=x^2\% \\ \Rightarrow \left[\frac{\mathrm{profit}}{\mathrm{CP}}\times 100\right]\%=x^2\% \\ \Rightarrow \left[\frac{\mathrm{profit}}{1200}\times 100\right]=x^2 \\ \Rightarrow \mathrm{profit}=\mathrm{Rs}12x^2 \\ \mathrm{Total}\mathrm{profit}=\mathrm{Rs}360 \\ \Rightarrow 12x+12x^2=360 \\ \Rightarrow 12\left[x^2+x-30\right]=0 \\ \Rightarrow x^2+x-30=0 \\ \Rightarrow x^2+6x-5x-30=0 \\ \Rightarrow x\left(x+6\right)-5\left(x+6\right)=0 \\ \Rightarrow \left(x-5\right)\left(x+6\right)=0 \\ \Rightarrow x-5=0\mathrm{or}x+6=0 \\ \Rightarrow x=5\mathrm{or}x=-6\left[\mathrm{rejected}\right] \\ \mathrm{So},\mathrm{profit}\mathrm{on}\mathrm{selling}\mathrm{first}\mathrm{article}=\mathrm{Rs}12x=\mathrm{Rs}60 \\ \Rightarrow \mathrm{SP}-\mathrm{CP}=60 \\ \Rightarrow \mathrm{SP}-1200=60 \\ \Rightarrow \mathbf{SP}\mathbf{}\mathbf{of}\mathbf{}\mathbf{first}\mathbf{}\mathbf{article}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Rs}\mathbf{}\mathbf{1260} \\ \mathrm{Now},\mathrm{profit}\mathrm{on}\mathrm{selling}\mathrm{second}\mathrm{article}=\mathrm{Rs}12x^2=\mathrm{Rs}300 \\ \Rightarrow \mathrm{SP}-\mathrm{CP}=300 \\ \Rightarrow \mathrm{SP}-1200=300 \\ \Rightarrow \mathbf{SP}\mathbf{}\mathbf{of}\mathbf{}\mathbf{second}\mathbf{}\mathbf{article}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Rs}\mathbf{}\mathbf{1500} \end{gathered}$$